Hi Boardies. I am interested in anything to do with the East Neuk of Fife, so I thought I would try and help with your query.
Those old headstones with faded inscriptions can be hard to read. John BROWN, father of Philip, died not in 1889, but in 1883, and if you want to look up his death-certificate, it's not in the parish of Elie, but in Earlsferry, parish of Kilconquhar. Although Elie and Earlsferry are physically joined up and to all intents and purposes one town, historically they are in different parishes.
Similarly, his wife Jane BROWN died, not in 1875, but in 1879.
They lived in Liberty Place, Earlsferry, par. of Kilconquhar, and can be seen there in the 1871 census. John was then a weaver, but his death-certificate gives him as "Seaman (Merchant Service)", and when his wife died in 1873 she was described as married to John BROWN, Seaman (Merchant Service).
Jane died on May 24th 1879, and her death was registered by her son Philip BROWN, of 112 West Fountainbridge, Edinburgh. Fountainbridge is just to the west of the city centre, and was the birthplace some years later of Sean "James Bond" Connery! I lived not far away myself at one time.
Philip gave his mother's parents as William BROWN, farm-servant, and Betsy ADAMSON.
John BROWN died on June 8th 1883, and his death was registered by his daughter Jane BROWN, "present", who gave his parents as William BROWN, fisherman, and Helen SCOTT.
Harry